Mastering Connect Four: The Solved Game Strategy

Connect Four is solved. James D. Allen and Victor Allis independently proved in 1988 that the first player wins with perfect play by starting in the center column. The proof does not make casual play easy — perfect play requires seeing 41 moves ahead — but it gives a clear roadmap. Mastering Connect Four means owning the center, building double threats, and pushing the opponent into positions where every move loses.

The 7×6 board

Connect Four is played on a 7-column, 6-row vertical board. Players alternate dropping discs into columns; discs fall to the lowest empty slot. First player to make four in a row (horizontal, vertical, or diagonal) wins. If the board fills with no winner, the game is a draw.

The solved result: the first player wins. The losing rate for the first player who plays optimally is zero. Any opening other than the center column loses against perfect play; the center column wins.

Why the center matters

The center column (column 4) is involved in more potential four-in-a-rows than any other column. Four of the seven possible horizontal lines pass through the center, every vertical four in column 4 is a threat, and all four major diagonals run through the center column at some height.

Casual opponents who let the first player take the center without a fight are giving up the game. A second player who lets the first player make a stack of three in the center is mostly already lost — the second player is forced to spend moves blocking, while the first player builds new threats elsewhere.

Odd and even threats

The most counter-intuitive idea in Connect Four is the parity of rows.

Because discs stack from the bottom up, a threat (three in a row that could complete) at a specific square is only relevant when the column below that square is full to that height. Threats in odd rows (rows 1, 3, 5 counting from the bottom) tend to favor the first player because the first player completes columns on odd-numbered moves. Even-row threats favor the second player.

Strong play involves creating threats on odd rows if you are the first player and on even rows if you are the second. Endgame zugzwang positions hinge on this parity: the player forced to fill a column up to a square where the opponent has a winning threat loses, and the threat parity decides which side is forced to lose.

The double threat

A double threat is two unrelated three-in-a-rows the opponent must block on the same move. They can only block one; the other completes. Double threats decide most Connect Four games at intermediate level.

Setting up a double threat usually requires three or four preparatory moves. The most common shape is a “fork” — a single disc that completes one row and starts another threat in a different direction. Spotting fork potential early is the practical skill that wins club games.

Defensive play involves spotting opponent forks before they exist and preempting them, either by blocking one of the future threats or by creating a counter-threat that forces the opponent to defend instead of attack.

Sacrifice moves

Sometimes the right move is to put a piece in a column that helps the opponent complete a three-in-a-row — because filling that square gives access to a winning square above it on your next move. This is a “sacrifice” or a “setup” move.

The pattern: you drop a disc in a column, knowing the opponent will play above it to make their own three. Their disc fills the next square up, which puts your previously-unreachable winning square within reach for your next move. You take the win the move after.

Sacrifice moves require seeing 3-5 moves ahead and being confident in the opponent’s reply. They are the source of the famous “long sequences” in Connect Four endgames.

Zugzwang and forced losses

Zugzwang is the position where every legal move loses. Connect Four positions reach zugzwang when the only columns still playable each fill a square that completes one of the opponent’s four-in-a-rows.

Strong play in the middlegame is partly about steering the position toward a zugzwang for the opponent. The classic technique is to leave open exactly one column the opponent can play in, with the height of that column rising to a row where you have a threat. Eventually the opponent is forced to play in that column and you win.

This is the “Claim Even” rule in some Connect Four literature: as the first player, claim threats on odd rows; as the second player, claim threats on even rows; force the opponent into positions where they must play into your threat parity.

Solved openings

Allis’s proof from 1988 (and Allen’s independent proof the same year) covers every starting move:

• Column 4 (center): wins for the first player.
• Columns 3 and 5: draws.
• Columns 2 and 6: losses for the first player.
• Columns 1 and 7: losses for the first player.

Symmetry makes columns 1 and 7, 2 and 6, 3 and 5 equivalent. Practically, the first player must play center; the second player must respond carefully but the win is not theirs — only the draw is achievable for the second player with perfect play against perfect first-player play.

Online perfect-play solvers (the Connect Four solver published with Allis’s thesis, plus several modern implementations) play the solved line and will explain every win for the first player.

Practical play tips

Most opponents do not play the solved line. Practical Connect Four against casual opponents rewards:

• Center control. Get to the center first, stack there as long as the opponent permits.
• Threat counting. Every move, identify every three-in-a-row both sides have and which row each threat completes on.
• Block immediate threats reactively, not preemptively. Spending moves blocking phantom threats wastes your tempo.
• Look for double-threat potential before defending. If you can attack and force the opponent to defend, do that.
• Calculate before you drop. Five moves of calculation finds the typical winning sequence in a clear-cut position.

Common mistakes

• Letting the first player take the center uncontested. If you are second, contest the center diagonally — block their vertical stack early.
• Missing the double threat the opponent is building. Every move you make, scan for opponent forks two moves away.
• Playing a sacrifice that helps the opponent. Sacrifices require the opponent’s reply to set up your winner; the wrong sacrifice just gives them a three.
• Ignoring threat parity. First player wants odd-row threats; second wants even. Mixing this up confuses the late-game zugzwang count.
• Playing fast. Most blunders happen because the move was made before the threat was counted.

How to practice

Online Connect Four solvers (the original Allis solver and several modern ones) let you play against perfect play. Losing every game against perfect play is normal; what matters is reviewing the moves where the solver says you made an error. After 50-100 games against a solver, the patterns of threats and double-threats become automatic.

For the proof of the solution and the proof technique (the “claimeven” and “baseinverse” rules), Victor Allis’s master’s thesis from 1988 is publicly available and is still the cleanest exposition. For the rules and history of the game, the Wikipedia article on Connect Four is a solid reference. For the rules walkthrough and basic tactics, see our how to win Connect Four guide. For similar pattern-completion games, see games like Connect Four.

Frequently asked questions

Is Connect Four solved?

Yes. James D. Allen and Victor Allis independently proved in 1988 that the first player wins with perfect play by starting in the center column. The full solution covers every position; perfect-play solvers are freely available online.

What is the best first move in Connect Four?

The center column (column 4 on a standard 7-wide board). Starting in the center wins with perfect play. Any other starting column draws or loses against optimal play.

Can the second player win in Connect Four?

Not against perfect play. The second player can draw if the first player makes a non-center opening, but cannot win against a first-player who plays the solved line. Against imperfect play, the second player wins routinely by punishing first-player mistakes.

What is a double threat in Connect Four?

A double threat is two three-in-a-rows the opponent must block on the same move. They can only block one; the other completes for the win. Building double threats is the standard offensive plan at intermediate level.

How long is the perfect-play sequence?

The first-player win starting from the center takes up to 41 moves in the longest variation. Most practical perfect-play games end sooner because the opponent makes a mistake along the way.

The bottom line

Mastering Connect Four is about owning the center, counting threats by row parity, and seeing double threats before they complete. The math says the first player wins; the practice says you have to find the winning moves over the board. When you need a break from threat-counting, the Chrome Dino game in the next tab requires no counting at all.

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